The given ratio is ke2Gmcmp
G= Gravitational constant
Its unit is Nm2kg−2.
me and mp= Masses of electron and proton.
Their unit is kg.
e= Electric charge.
Its unit is C.
∈0= Permittivity of free space
Its unit is Nm2C−2.
Unit of the given ratio ke2Gmcmp=[Nm2C2][C−2][Nm2kg−2][kg][kg]
Hence, the given ratio is dimensionless.
This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.